1 . 如图,在四棱柱
中,侧棱
底面
,![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/be78c87a12bd4f178ff6a4c0f04bcd39.png?resizew=369)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/6ed0029709a24466bd9e69a353fb805f.png?resizew=165)
(Ⅰ)求证:
平面![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/ecfecb375d3f489b96b19680c8bd699d.png?resizew=52)
(Ⅱ)若直线
与平面
所成角的正弦值为
,求
的值
(Ⅲ)现将与四棱柱
形状和大小完全相同的两个四棱柱拼成一个新的四棱柱,规定:若拼成的新四棱柱形状和大小完全相同,则视为同一种拼接方案,问共有几种不同的拼接方案?在这些拼接成的新四棱柱中,记其中最小的表面积为
,写出
的解析式.(直接写出答案,不必说明理由)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/e9515fa586c3440294998e93ea73c2ad.png?resizew=109)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/840c8a5a421d4aa6b738f39edecf297b.png?resizew=40)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/0c60d2348ff0423aaaae6726f5b175b8.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/be78c87a12bd4f178ff6a4c0f04bcd39.png?resizew=369)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/6ed0029709a24466bd9e69a353fb805f.png?resizew=165)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/520a3d70f9b64e3ca1c123d2561c15ba.png?resizew=39)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/ecfecb375d3f489b96b19680c8bd699d.png?resizew=52)
(Ⅱ)若直线
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/4ceb59de4bb642b2ba77a9beb79f82ff.png?resizew=27)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/60c4e518780641fd95d2caf9ed1f39d2.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/3d5150f6dd58437885fe1b8ea86112a1.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/443501c59e8849d1b4fe2509b1d390c5.png?resizew=13)
(Ⅲ)现将与四棱柱
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/e9515fa586c3440294998e93ea73c2ad.png?resizew=109)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/c531fed82aec405c8e208b8ea71dca7b.png?resizew=33)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571285821030400/1571285826789376/STEM/c531fed82aec405c8e208b8ea71dca7b.png?resizew=33)
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